In molecular physics, the van der Waals forces, named after Dutch
scientist Johannes Diderik van der Waals, are distance-dependent
interactions between atoms or molecules. Unlike ionic or covalent
bonds, these attractions are not a result of any chemical electronic
bond, and they are comparatively weak and more susceptible to being
perturbed. Van der Waals forces quickly vanish at longer distances
between interacting molecules.
Van der Waals forces play a fundamental role in fields as diverse as
supramolecular chemistry, structural biology, polymer science,
nanotechnology, surface science, and condensed matter physics. Van der
Waals forces also define many properties of organic compounds and
molecular solids, including their solubility in polar and non-polar
media.
If no other forces are present, the point at which the force becomes
repulsive rather than attractive as two atoms near one another is
called the van der Waals contact distance. This results from the
electron clouds of two atoms unfavorably coming into contact.[1] It
can be shown that van der Waals forces are of the same origin as that
of the Casimir effect, arising from quantum interactions with the
zero-point field.[2] The resulting van der Waals forces can be
attractive or repulsive.[3] Term "Van der Waals forces" is also
sometimes used loosely as a synonym for the totality of intermolecular
forces.[4] The term always includes the force between instantaneously
induced dipoles (London dispersion force), sometimes includes the
force between a permanent dipole and a corresponding induced dipole
(Debye force), and – less frequently – includes the force between
permanent dipoles (Keesom force).

Definition[edit]
Van der Waals forces include attraction and repulsions between atoms,
molecules, and surfaces, as well as other intermolecular forces. They
differ from covalent and ionic bonding in that they are caused by
correlations in the fluctuating polarizations of nearby particles (a
consequence of quantum dynamics[5]).
Being the weakest of the weak chemical forces, with a strength between
0.4 and 4kJ/mol they may still support an integral structural load
when multitudes of such interactions are present. Such a force results
from a transient shift in electron density. Specifically, as the
electrons are in orbit of the protons and neutrons within an atom the
electron density may tend to shift more greatly on a side. Thus, this
generates a transient charge to which a nearby atom can be either
attracted or repelled. When the interatomic distance of two atoms is
greater than 0.6 nm the force is not strong enough to be
observed. In the same vein, when the interatomic distance is below
0.4 nm the force becomes repulsive.
Intermolecular forcesIntermolecular forces have four major contributions:

A repulsive component resulting from the Pauli exclusion principle
that prevents the collapse of molecules.
Attractive or repulsive electrostatic interactions between permanent
charges (in the case of molecular ions), dipoles (in the case of
molecules without inversion center), quadrupoles (all molecules with
symmetry lower than cubic), and in general between permanent
multipoles. The electrostatic interaction is sometimes called the
Keesom interaction or
Keesom forceKeesom force after Willem Hendrik Keesom.
Induction (also known as polarization), which is the attractive
interaction between a permanent multipole on one molecule with an
induced multipole on another. This interaction is sometimes called
Debye forceDebye force after Peter J.W. Debye.
Dispersion (usually named London dispersion interactions after Fritz
London), which is the attractive interaction between any pair of
molecules, including non-polar atoms, arising from the interactions of
instantaneous multipoles.

Returning to nomenclature, different texts refer to different things
using the term "van der Waals force". Some texts describe the van der
Waals force as the totality of forces (including repulsion); others
mean all the attractive forces (and then sometimes distinguish van der
Waals-Keesom, van der Waals-Debye, and van der Waals-London).
All intermolecular/van der Waals forces are anisotropic (except those
between two noble gas atoms), which means that they depend on the
relative orientation of the molecules. The induction and dispersion
interactions are always attractive, irrespective of orientation, but
the electrostatic interaction changes sign upon rotation of the
molecules. That is, the electrostatic force can be attractive or
repulsive, depending on the mutual orientation of the molecules. When
molecules are in thermal motion, as they are in the gas and liquid
phase, the electrostatic force is averaged out to a large extent,
because the molecules thermally rotate and thus probe both repulsive
and attractive parts of the electrostatic force. Sometimes this effect
is expressed by the statement that "random thermal motion around room
temperature can usually overcome or disrupt them" (which refers to the
electrostatic component of the van der Waals force). Clearly, the
thermal averaging effect is much less pronounced for the attractive
induction and dispersion forces.
The
Lennard-Jones potentialLennard-Jones potential is often used as an approximate model for
the isotropic part of a total (repulsion plus attraction) van der
Waals force as a function of distance.
van der Waals forces are responsible for certain cases of pressure
broadening (van der Waals broadening) of spectral lines and the
formation of van der Waals molecules. The London-van der Waals forces
are related to the
Casimir effectCasimir effect for dielectric media, the former
being the microscopic description of the latter bulk property. The
first detailed calculations of this were done in 1955 by E. M.
Lifshitz.[6] A more general theory of van der Waals forces has also
been developed.[7][8]
The main characteristics of van der Waals forces are:[9]

They are weaker than normal covalent and ionic bonds.
van der Waals forces are additive and cannot be saturated.
They have no directional characteristic.
They are all short-range forces and hence only interactions between
the nearest particles need to be considered (instead of all the
particles). Van der Waals attraction is greater if the molecules are
closer.
van der Waals forces are independent of temperature except dipole –
dipole interactions.

In low molecular weight alcohols, the hydrogen-bonding properties of
their polar hydroxyl group dominate other weaker van der Waals
interactions. In higher molecular weight alcohols, the properties of
the nonpolar hydrocarbon chain(s) dominate and define the solubility.
London dispersion force[edit]
Main article: London dispersion force
London dispersion forces, named after the German-American physicist
Fritz London, are weak intermolecular forces that arise from the
interactive forces between instantaneous multipoles in molecules
without permanent multipole moments. These forces dominate the
interaction of non-polar molecules, and are often more significant
than Keesom and Debye forces in polar molecules. London dispersion
forces are also known as 'dispersion forces', 'London forces', or
'instantaneous dipole–induced dipole forces'. The strength of London
dispersion forces is proportional to the polarizability of the
molecule, which in turn depends on the total number of electrons and
the area over which they are spread. Any connection between the
strength of London dispersion forces and mass is coincidental.
van der Waals forces between macroscopic objects[edit]
For macroscopic bodies with known volumes and numbers of atoms or
molecules per unit volume, the total van der Waals force is often
computed based on the "microscopic theory" as the sum over all
interacting pairs. It is necessary to integrate over the total volume
of the object, which makes the calculation dependent on the objects'
shapes. For example, the van der Waals' interaction energy between
spherical bodies of radii R1 and R2 and with smooth surfaces was
approximated in 1937 by Hamaker[10] (using London's famous 1937
equation for the dispersion interaction energy between
atoms/molecules[11] as the starting point) by:

where A is the Hamaker coefficient, which is a constant (~10−19 −
10−20 J) that depends on the material properties (it can be positive
or negative in sign depending on the intervening medium), and z is the
center-to-center distance; i.e., the sum of R1, R2, and r (the
distance between the surfaces):

z
=

R

1

+

R

2

+
r

displaystyle z=R_ 1 +R_ 2 +r

.
In the limit of close-approach, the spheres are sufficiently large
compared to the distance between them; i.e.,

r
≪

R

1

displaystyle rll R_ 1

or

R

2

displaystyle R_ 2

, so that equation (1) for the potential energy function simplifies
to:

U
(
r
;

R

1

,

R

2

)
=
−

A

R

1

R

2

(

R

1

+

R

2

)
6
r

displaystyle U(r;R_ 1 ,R_ 2 )=- frac AR_ 1 R_ 2 (R_ 1 +R_ 2
)6r

(2)

The van der Waals force between two spheres of constant radii (R1 and
R2 are treated as parameters) is then a function of separation since
the force on an object is the negative of the derivative of the
potential energy function,

F

V
W

(
r
)
=
−

d

d
r

U
(
r
)

displaystyle F_ VW (r)=- frac d dr U(r)

. This yields:

F

V
W

(
r
)
=
−

A

R

1

R

2

(

R

1

+

R

2

)
6

r

2

displaystyle F_ VW (r)=- frac AR_ 1 R_ 2 (R_ 1 +R_ 2 )6r^ 2

(3)

The van der Waals forces between objects with other geometries using
the Hamaker model have been published in the literature.[12][13][14]
From the expression above, it is seen that the van der Waals force
decreases with decreasing size of bodies (R). Nevertheless, the
strength of inertial forces, such as gravity and drag/lift, decrease
to a greater extent. Consequently, the van der Waals forces become
dominant for collections of very small particles such as very
fine-grained dry powders (where there are no capillary forces present)
even though the force of attraction is smaller in magnitude than it is
for larger particles of the same substance. Such powders are said to
be cohesive, meaning they are not as easily fluidized or pneumatically
conveyed as their more coarse-grained counterparts. Generally,
free-flow occurs with particles greater than about 250 μm.
The van der Waals force of adhesion is also dependent on the surface
topography. If there are surface asperities, or protuberances, that
result in a greater total area of contact between two particles or
between a particle and a wall, this increases the van der Waals force
of attraction as well as the tendency for mechanical interlocking.
The microscopic theory assumes pairwise additivity. It neglects
many-body interactions and retardation. A more rigorous approach
accounting for these effects, called the "macroscopic theory" was
developed by Lifshitz in 1956.[15] Langbein derived a much more
cumbersome "exact" expression in 1970 for spherical bodies within the
framework of the Lifshitz theory[16] while a simpler macroscopic model
approximation had been made by Derjaguin as early as 1934.[17]
Expressions for the van der Waals forces for many different geometries
using the Lifshitz theory have likewise been published.
Use by geckos and arthropods[edit]

Further information:
ArthropodArthropod adhesion
The ability of geckos – which can hang on a glass surface using only
one toe – to climb on sheer surfaces has been attributed to the van
der Waals forces between these surfaces and the spatulae, or
microscopic projections, which cover the hair-like setae found on
their footpads.[18][19] A later study suggested that capillary
adhesion might play a role,[20] but that hypothesis has been rejected
by more recent studies.[21][22][23] There were efforts in 2008 to
create a dry glue that exploits the effect,[24] and success was
achieved in 2011 to create an adhesive tape on similar grounds.[25] In
2011, a paper was published relating the effect to both velcro-like
hairs and the presence of lipids in gecko footprints.[26]
Among the arthropods, some spiders have similar setae on their
scopulae or scopula pads, enabling them to climb or hang upside-down
from extremely smooth surfaces such as glass or porcelain.[27][28]
In modern technology[edit]
In May 2014, DARPA demonstrated the latest iteration of its Geckskin
by having a 100 kg researcher (saddled with 20 kg of
recording gear) scale an 8-metre-tall (26 ft) glass wall using
only two climbing paddles. Tests are ongoing, but DARPA hopes one day
to make the technology available for military use, giving soldiers
Spider Man-like abilities in urban combat.[29]
See also[edit]